The four leaf clover has nothing to do with the Irish. It is because people talk about the luck of the Irish that people assume its Irish. It is actually the normal 3 leaf clover that is Irish. St Patrick used it to represent the cross.
It is a three-leafed, old white clover. It is sometimes of the variety Trifolium repens (a white clover, known in Irish as seamair bhán) but today usually Trifolium dubium (a lesser clover, Irish: seamair bhuí).
back in the day, Boston was full of Irish men. The founder of the team put them in green uniform and called them the Boston Celtics. The clover design is is derived from the Irish culture, since Boston was mostly populated with Irish people.